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Linear Codes and Polylinear Recurrences over Finite Rings and Modules (A Survey)статья
Информация о цитировании статьи получена из
Web of Science
Дата последнего поиска статьи во внешних источниках: 27 мая 2015 г.
- Авторы: Kurakin V.L., Kuzmin A.S., Markov V.T., Mikhalev A.V., Nechaev A.A.
- Сборник: Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
- Серия: Lecture Notes in Computer Science
- Том: 1719
- Год издания: 1999
- Место издания: Springer Berlin Heidelberg
- Первая страница: 365
- Последняя страница: 390
- DOI: 10.1007/3-540-46796-3_36
- Аннотация: We give a short survey of the results obtained in the last several decades that develop the theory of linear codes and polylinear recurrences over finite rings and modules following the well-known results on codes and polylinear recurrences over finite fields. The first direction contains the general results of theory of linear codes, including: the concepts of a reciprocal code and the MacWilliams identity; comparison of linear code properties over fields and over modules; study of weight functions on finite modules, that generalize in some natural way the Hamming weight on a finite field; the ways of representation of codes over fields by linear codes over modules. The second one develops the general theory of polylinear recurrences; describes the algebraic relations between the families of linear recurrent sequences and their periodic properties; studies the ways of obtaining “good” pseudorandom sequences from them. The interaction of these two directions leads to the results on the representation of linear codes by polylinear recurrences and to the constructions of recursive MDS-codes. The common algebraic foundation for the effective development of both directions is the Morita duality theory based on the concept of a quasi-Frobenius module.
- Добавил в систему: Нечаев Александр Александрович